The El Niño/Southern Oscillation (ENSO) phenomenon is the dominant climatic fluctuation on interannual time scales. It is an irregular oscillation with a distinctive broadband spectrum. In this article, we discuss recent theories that seek to explain this irregularity. Particular attention is paid to explanations that involve the stochastic forcing of the slow ocean modes by fast atmospheric transients. We present a theoretical framework for analysing this picture of the irregularity and also discuss the results from a number of coupled ocean-atmosphere models. Finally, we briefly review the implications of the various explanations of ENSO irregularity to attempts to predict this economically significant phenomenon.